Weighted Block L1 Norm Regularized Two-dimensional Off-grid Compressive Beamforming for Acoustic Source Identification

High spatial resolution and high accuracy acoustic source identification is valuable in the field of aircraft. Compressive beamforming is a potential method to achieve a high-quality acoustic map. However, the off-grid problem and convex relaxation loss will reduce the performance of compressive beamforming. The weighted block L1 norm regularized two-dimensional (2D) off-grid beamforming method is proposed in this paper. In the proposed method, the solution containing the source amplitudes and off-grid differences is constrained by the weighted block L1 norm. The weighted block L1 norm can induce a more sparse solution to enhance the spatial resolution of the obtained acoustic map. Moreover, it can also recover the source amplitudes more accurately due to the fair penalty value. The performance of the proposed method is also validated by a numerical simulation. It turns out that the proposed method can identify the acoustic sources with higher spatial resolution and higher accuracy compared with conventional compressive beamforming methods.